CN110046436B - Spacecraft autonomous measurement and control coverage analysis method - Google Patents
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Abstract
The invention relates to an autonomous measurement and control coverage analysis method for a spacecraft, which comprises the following steps: a. establishing a ground station coordinate system for describing relative station movement of a spacecraft to a ground designated point, establishing a geocentric equatorial fixed coordinate system, and establishing an orthogonal transformation matrix from the station coordinate system to the fixed coordinate system; b. calculating boundary conditions of the spacecraft which can be covered by the measuring station; c. and (c) performing measurement and control coverage calculation according to the measurement and control coverage boundary conditions in the step (b). The spacecraft autonomous measurement and control coverage analysis method accurately calculates the time of entering and exiting the station, and the algorithm only involves simple matrix operation and trigonometric function operation, so that numerical integration and point-by-point measurement and control coverage analysis are avoided, the calculated amount is greatly reduced, and the reliability is improved. The method is suitable for on-orbit autonomous measurement and control coverage analysis of the spacecraft.
Description
Technical Field
The invention relates to an autonomous measurement and control coverage analysis method for a spacecraft.
Background
The spacecraft for executing the flight mission has the mission arrangement determined by the flight scheme in the design stage, such as the events of flight state setting, orbit control strategy planning, equipment on-orbit test, intersection butt joint execution and the like. Because these events are closely related to factors such as flight control results, task tracks, measurement and control coverage, etc., the specific time of execution cannot be determined in the design stage, and the events need to be completed in the flight tasks through real-time control.
Flight control of a spacecraft generally includes two approaches: a heaven and earth large loop control mode based on ground measurement and control and an on-orbit autonomous control mode based on a spacecraft self-platform. Currently, the flight control of most spacecraft adopts the former: the design unit designs a flight program according to task requirements and constraint conditions; the implementation unit combines the real-time orbit determination result according to the flight program to generate a flight program which accords with the actual measurement and control constraint and injects the flight program into the spacecraft; the injected data also needs multiparty checking, and the flow is very complex. The future space launching task presents new challenges for flight control, taking a manned spacecraft which participates in space station construction and operation as an example, on one hand, due to timeliness constraint, the unmanned aerial vehicle needs to have the capability of rapid intersection and docking; on the other hand, in consideration of maintenance requirements of space stations, the flying back and forth between the sky and the earth is frequent, and the emission density is increased. If the traditional flight control mode is continuously adopted, the occupation amount of manpower and material resources is continuously increased. In order to reduce the complexity of operation, shorten the flight procedure generation time, reduce the cost of tasks, simplify the ground support system, realize the autonomous control of spacecraft on orbit and be the big trend of future spacecraft development.
And the spacecraft is automatically controlled, and the spacecraft is required to automatically complete conversion processing from the mission-class user requirements to the flight program by adopting a certain algorithm. The flight procedure of a spacecraft mainly comprises two parts of contents: in and out of the measurement and control zone program and an event program for executing specific tasks. The former is used for opening or closing the world link communication equipment when entering or exiting the measurement and control area; the latter executes specific events of the flight mission arrangement, such as a switch of a rail-controlled engine, a maintenance of a docking point in a meeting docking, a docking contact and the like, and most key events are bound with the moment of entering and exiting a measurement and control area. Therefore, the autonomous measurement and control coverage calculation is an important link for realizing autonomous flight program planning of the spacecraft.
Disclosure of Invention
The invention aims to solve the problems, accurately calculate the time for entering and exiting the station of the spacecraft, reduce the calculated amount of the spacecraft autonomous measurement and control coverage analysis method and improve the reliability of the spacecraft autonomous measurement and control coverage analysis method.
In order to achieve the aim of the invention, the invention provides a spacecraft autonomous measurement and control coverage analysis method, which comprises the following steps: a. establishing a ground station coordinate system for describing relative station movement of a spacecraft to a ground designated point, establishing a geocentric equatorial fixed coordinate system, and establishing an orthogonal transformation matrix from the station coordinate system to the fixed coordinate system;
b. calculating boundary conditions of the spacecraft which can be covered by the measuring station;
c. and (c) performing measurement and control coverage calculation according to the measurement and control coverage boundary conditions in the step (b).
According to one aspect of the invention, in the step b, according to the parameter of the station under the fixed connection coordinate system and the orbit parameter of the observed spacecraft, the longitude and latitude amplitude angles of the boundary lifting intersection point which can be observed by the station of the spacecraft are obtained, and the future circle number of the station of the spacecraft is obtained;
and solving the earth center distance of the spacecraft when the spacecraft passes through the station according to the orbit parameters of the observed spacecraft.
According to one aspect of the invention, in the step c, according to the circle number, the latitude amplitude angle and the geodetic distance when the station is oversteered obtained in the step b, the orbit of the spacecraft is directly extrapolated to the rough moment of the station by using an autonomous orbit prediction algorithm; and on the basis of the rough moment of the station passing by, the moment of entering and exiting the station and the station passing time are accurately calculated.
According to one aspect of the invention, in the step a, the station coordinate system is used for describing the movement of the spacecraft relative to the station for a ground designated point; origin o of coordinate system of measuring station s Taking the center of the measuring station and z when the earth is spherical s The axis points from the earth center to the zenith, x s Axis, y s The axis is positioned in the local horizontal plane, is parallel to the meridian line and the weft line of the passing station respectively, and points to the eastern and the north respectively;
the reference plane of the fixedly connected coordinate system is a protocol equatorial plane, the x-axis points to the Greennel meridian, the z-axis points to the international protocol origin CIO, and the x-axis, the y-axis and the z-axis form a right-hand system;
the longitude of the measuring station under the fixed coordinate system is lambda, and the latitude is
The average radius of the earth is R, the coordinate system of the measuring station is connected to the fixed connection seatThe orthogonal transformation matrix E of the standard system is:
vector r of geodetic centre pointing to measuring station s The attached coordinate system can be expressed as:
according to one aspect of the invention, in the step b, the measurement and control coverage boundary condition of a single measuring station on the spacecraft is solved, and the longitude omega of the ascending intersection point of the trajectory of the point under the boundary satellite which can be observed by the measuring station S of the spacecraft and the corresponding latitude amplitude phi are solved according to the position of the measuring station S, the lowest measurement and control elevation angle alpha and the orbit number of the observed spacecraft t.
According to one aspect of the invention, the boundary orbit parameters are solved, and the longitude lambda and latitude of the station S under the fixed coordinate system are measured
The lowest elevation angle of the station is alpha; the ground center distance of the observed spacecraft t is r, the orbit inclination angle is i, and the longitude omega of the boundary lifting intersection point observed by the observed station S of the spacecraft t is solved 1 And omega 3 The method is characterized by comprising the following steps:
(1) solving unit speed vector v of spacecraft when being positioned at measurement and control boundary
In the coordinate system of the measuring station, the vector r of the measuring station pointing to the spacecraft st Can be expressed as:
wherein the variable θ is introduced, defined as r xy And y is s An included angle of the shaft;
in the coordinate system of the measuring station, the measuring station position vector r s Can be expressed as:
wherein R is the average radius of the earth;
in the station coordinate system, the unit velocity vector v can be expressed as:
(2) solving a normal vector h of a track surface of the spacecraft when being positioned at a measurement and control boundary
In the station coordinate system, spacecraft position vector r t Can be expressed as:
the track plane normal vector h can be expressed as:
note that |h|=rcosα, normalized by h yields a unit vector:
(3) solving for the variable θ using equality constraints
In the coordinate system of the measuring station, the unit vector z corresponding to the z axis of the fixed coordinate system can be expressed as:
the included angle between the normal unit vector h of the track surface and the unit vector z is the track inclination angle i, and can be determined by the following formula:
θ can be solved according to the above:
wherein the value range of the inverse cosine function is [0, pi ]]Two solutions of θ obtained in the formula 1 、θ 3 Corresponding to the spacecraft circle satellite point tracks L which just pass through the measurement and control boundary respectively 1 And L 3 ；
(4) Calculating track lifting intersection longitude
The coordinate system descending intersection vector N can be obtained by the following formula:
the track lifting intersection longitude Ω' is obtained from the following two:
by solving for θ by two solutions of θ 1 、θ 3 Substituting formula I and finding omega 'from formula II' 1 、Ω′ 3 ；
(5) Calculating latitude amplitude angle of spacecraft when being positioned at measurement and control boundary
The latitude amplitude angle phi is an ascending intersection line vector N and a spacecraft position vector r t The included angle between the two parts is that,
and (5) obtaining the inverse cosine:
when the measuring station is positioned in the northern hemisphere, the value range of the inverse cosine function is [0, pi ]]Through two solutions of θ 1 、θ 3 Substitution to obtain two solutions of phi 1 、Φ 3 ；
(6) Calculating the longitude of the ascending intersection point of the track of the point under the satellite
Considering the rotation of the earth and the right ascent and descent of the orbit intersection point of the spacecraft, the longitude of the orbit intersection point of the satellite point of the spacecraft is not equal to the longitude of the orbit intersection point, the latitude amplitude angle when the spacecraft passes the boundary of the measuring station is phi, and the orbit period is T, the time difference deltat between the moment of the orbit intersection point of the spacecraft passing the circle and the current moment is known as:
when the spacecraft passes the station boundary, the longitude of the orbit intersection point is omega', and when the longitude of the orbit intersection point of the ring star lower point is omega:
wherein omega e Is the rotation angular rate of the earth;
for increasing the intersection right-hand drift rate, it is determined by the following formula:
wherein a is e The radius of the equator of the earth, a is the semilong axis of the orbit, e is the eccentricity of the orbit, and the unit of the above formula is (°)/d;
by the steps (1) to (6), the boundary rise intersection point longitude Ω of the spacecraft t that can be observed by the station S is obtained 1 And omega 3 。
According to one aspect of the invention, the number of passes of a spacecraft station is solved: t is t 0 The longitude of the orbit ascending intersection point of the time spacecraft is omega' 0 The track circle number is N 0 After n more turns, the future turn number of the passing measuring station can be obtained by the following formula:
after n is solved by the method, the station ring can be obtainedSecondary is N 0 +n。
According to one aspect of the invention, solving for spacecraft ground distances: when the spacecraft passes through the station roof, the vector pointing to the spacecraft from the station is r s At this time, r s In the plane of the spacecraft orbit, in the station coordinate system, the normal unit vector of the spacecraft orbit can be expressed as:
wherein θ is a free variable;
the relationship between the track inclination angles i and h and the unit vector z corresponding to the z axis of the fixed coordinate system can be expressed as follows:
θ can be obtained from the above:
the ascending intersection line N of the spacecraft orbit is as follows:
when the measuring station is positioned in the northern hemisphere, the latitude amplitude angle phi when the spacecraft passes the measuring station top is as follows:
the ground center distance when the spacecraft passes the station is as follows:
according to one aspect of the invention, in the step c, autonomous orbit prediction is included, and orbit extrapolation is performed by adopting a pseudo-average root number method;
for global aspheric gravitational perturbation, the non-singular perturbation solution is expressed as formula three:
in the first order sense, the form is of formula four:
wherein sigma (t) is the instantaneous orbit number,
for the average number of tracks, < > is->
Is a first order short period term,/->
Is a second-order short period term, sigma 1 As a first-order long term, sigma 2 For long term of second order>
Is a first-order long period term, t 0 Representing an initial time;
the low-orbit manned spacecraft needs to consider the atmospheric resistance, and an average density model can be adopted to construct an atmospheric resistance perturbation solution; substituting the atmospheric resistance perturbation as a second-order long term into the formula 1 in the fourth, so as to obtain an orbit extrapolation analytical expression considering the global aspheric gravitation and the atmospheric resistance;
the autonomous orbit prediction procedure is thus available as follows: when the spacecraft obtains t through autonomous orbit determination 0 Instantaneous orbit root sigma of moment 0 Then, the average track number corresponding to the moment is obtained by the 3 rd expression in the fourth expression
Obtaining the average track number of any time t according to the 1 st expression and each order perturbation expression in the fourth expression>
Finally, the instantaneous orbit root sigma (t) at the moment t is obtained according to the formula III.
According to one aspect of the invention, in the step c, the time for entering and exiting the station is calculated, namely, the time period that the elevation angle of the spacecraft relative to the station is larger than the lowest elevation angle alpha of the station is calculated;
the elevation angle of the spacecraft at any moment relative to the measuring station is as follows:
the whole process of spacecraft orbit propulsion is discretized into m equal parts, namely m+1 discrete points, and the corresponding time sequence is recorded as t i I=1, 2, …, m+1; obtaining the difference delta between the elevation angle of the spacecraft relative to the measuring station at m+1 points and the minimum observation elevation angle; when delta i Not less than 0 and delta i-1 <At 0, t i The time for starting measurement and control; when delta i <0 and delta i-1 When not less than 0, t i The time of the end of measurement and control; because of the discrete processing, only a conservative estimation of the actual measurement and control start or end time is performed, and for better approximation, linear interpolation can be performed, wherein the actual measurement and control start or end time is t' i This time must be in interval t i-1 ，t i ]In, the corresponding elevation angle difference is 0, and the following conditions are satisfied on the premise that the elevation angle linearly changes along with time:
thereby obtaining the following steps:
according to the spacecraft autonomous measurement and control coverage analysis method, the orbit circle number and latitude amplitude range of a future over-measurement station of the spacecraft are determined by solving the measurement and control boundary conditions of the over-measurement station; the orbit of the spacecraft is directly extrapolated to the station-passing moment from the current moment by using the extrapolation of the orbit of the analytic method, and the time for entering and exiting the station is accurately calculated on the basis. The algorithm only involves simple matrix operation and trigonometric function operation, avoids numerical integration and point-by-point measurement and control coverage analysis, greatly reduces the calculated amount and improves the reliability. The method is suitable for on-orbit autonomous measurement and control coverage analysis of the spacecraft.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 schematically shows a flow chart of a spacecraft autonomous measurement and control coverage analysis method according to the invention;
FIG. 2 schematically illustrates a graph of positional relationship in a coordinate system of a station according to one embodiment of the invention;
FIG. 3 schematically illustrates a positional relationship under an attached coordinate system according to an embodiment of the present invention;
FIG. 4 schematically illustrates a plot of points below the satellite as the spacecraft crosses the measurement and control boundary, in accordance with an embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments will be briefly described below. It is apparent that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
In describing embodiments of the present invention, the terms "longitudinal," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in terms of orientation or positional relationship shown in the drawings for convenience of description and simplicity of description only, and do not denote or imply that the devices or elements in question must have a particular orientation, be constructed and operated in a particular orientation, so that the above terms are not to be construed as limiting the invention.
The present invention will be described in detail below with reference to the drawings and the specific embodiments, which are not described in detail herein, but the embodiments of the present invention are not limited to the following embodiments.
Fig. 1 schematically shows a flow chart of a spacecraft autonomous measurement coverage analysis method according to the invention. As shown in fig. 1, the spacecraft autonomous measurement and control coverage analysis method according to the invention comprises the following steps:
a. establishing a coordinate system and a coordinate conversion relation;
b. calculating boundary conditions which can be covered by the measurement and control of the station to be measured of the spacecraft;
c. and c, performing measurement and control coverage calculation according to the measurement and control coverage boundary conditions in the step b.
The method for establishing the coordinate system and the coordinate conversion relation comprises the following steps: establishing a ground station coordinate system for describing relative station motion of the spacecraft to a ground designated point, establishing a geocentric equatorial fixed connection coordinate system, and establishing an orthogonal transformation matrix from the station coordinate system to the fixed connection coordinate system.
The station coordinate system is used to describe the movement of the spacecraft relative to the station for a ground designated point. Measuring station coordinate system origin o s Taking the center of the measuring station and z when the earth is spherical s The axis points from the earth center to the zenith, x s Axis, y s The axes are positioned in the local horizontal plane, are respectively parallel to the meridian line and the latitude line of the passing station, and are respectively directed to the eastern and the north.
The reference plane of the fixed coordinate system is a protocol equatorial plane, the x-axis points to the Greennel meridian, the z-axis points to the international protocol origin CIO, and the x-axis, the y-axis and the z-axis form a right-hand system.
The longitude of the measuring station under the fixed coordinate system is lambda, and the latitude is
The average radius of the earth is RThe orthogonal transformation matrix E from the station coordinate system to the fixed connection coordinate system is as follows:
vector r of geodetic centre pointing to measuring station s The following can be expressed in terms of the attached coordinate system:
b. calculating boundary conditions of the spacecraft which can be covered by the station measurement and control comprises the following steps: and according to the parameters of the measuring station under the fixed connection coordinate system and the orbit parameters of the observed spacecraft, solving the longitude and latitude amplitude angles of the boundary lifting intersection point which can be observed by the measuring station of the spacecraft, and obtaining the future circle number of the future passing measuring station of the spacecraft.
The method solves the measurement and control coverage boundary condition of a single measuring station on the spacecraft, and specifically solves the longitude omega of the ascending intersection point of the trajectory of the point under the boundary satellite, which can be observed by the measuring station S, and the latitude amplitude phi corresponding to the spacecraft according to the position of the measuring station S, the lowest measurement and control elevation angle alpha and the orbit number of the observed spacecraft t.
In order to obtain the measurement and control coverage range of the measurement and control station to the spacecraft, firstly, the spacecraft orbit passing through the measurement and control boundary is considered. The method is characterized in that the undersea point of the spacecraft is defined as the projection of the spacecraft on the surface of the earth, and the track formed by the undersea point moving along with the spacecraft is the undersea point track. When the semimajor axis, the eccentricity, the near-place amplitude angle and the track inclination angle in the track number are determined, the shape of the track of the satellite lower point is determined immediately, and the position of the track of the satellite lower point is determined by the longitude of the ascending intersection point. For simplifying analysis, the apparent earth is spherical, and the orbit of the apparent spacecraft is a nearly circular orbit without losing generality. The positional relationship between the spacecraft and the measuring station when the spacecraft passes the measuring station to measure and control the boundary is shown in fig. 2, 3 and 4.
Fig. 2 is a positional relationship diagram in a coordinate system of a measuring station, fig. 3 is a positional relationship diagram in a fixed coordinate system, and fig. 4 is a positional relationship diagram of a track of a point under a satellite. Wherein o is the earth center, S is the station, t is the spacecraft, alpha is the lowest elevation angle of the station, r t For spacecraft position vectorsQuantity, r s For measuring station position vector r st The vector pointing to the spacecraft for the station is h is the orbit normal vector.
Fig. 4 shows the trajectory of the points under the satellite when the spacecraft crosses the station boundary in the station coordinate system, all the points under the spacecraft located at the measurement and control boundary (when the station is viewed at the lowest elevation angle) constituting the measurement and control boundary trajectory of the station, the projection of which on the earth surface is a circle. The dotted line is the spacecraft circle star point track (L) 1 ～L 4 4 in total), at the moment, the measurement and control boundary track is tangent with the spacecraft point track under the star. The longitude of the ascending intersection point corresponding to the track of the point under the satellite is omega respectively 1 、Ω 2 、Ω 3 、Ω 4 . v is the velocity vector when passing the measurement and control boundary, r xy R is st At x s y s Projection in a plane. From the figure, when the station position is known, for a spacecraft with a specific orbit altitude and orbit inclination, when the intersection point of the track rise of a certain circle of the spacecraft is located at [ omega ], the longitude omega of the intersection point of the track rise of the certain circle of the spacecraft is located at [ omega ] 1 ,Ω 2 ]Or [ omega ] 4 ,Ω 3 ]When it is, it can be considered that its circle is observable by the station under test.
The following is a boundary orbit parameter solving process.
Knowing the longitude lambda and latitude of the station S under the fixed coordinate system
The lowest elevation angle of the station is alpha; the ground center distance of the observed spacecraft t is r (for a near-circular orbit, the semi-long axis a can be used for replacing the observed spacecraft t), the orbit inclination angle is i, and the longitude omega of the boundary lifting intersection point of the observed spacecraft t which can be observed by the station S is solved 1 、Ω 2 、Ω 3 、Ω 4 . The invention only gives omega 1 、Ω 3 Solving step of (a) solving Ω 2 、Ω 4 The corresponding formulas in the calculation process only need to be opposite in sign. The method comprises the following steps:
(1) solving unit speed vector v of spacecraft when being positioned at measurement and control boundary
In the coordinate system of the measuring station, the vector r of the measuring station pointing to the spacecraft st Can be expressed as:
wherein the variable θ is introduced, defined as r xy And y is s An included angle of the shaft; r is (r) st R is st The modulus of (2) is a known quantity, and can be obtained from R, α, and R by using the cosine law according to fig. 2.
In the coordinate system of the measuring station, the measuring station position vector r s Can be expressed as:
wherein R is the average radius of the earth;
in the station coordinate system, the unit velocity vector v can be expressed as:
(2) solving a normal vector h of a track surface of the spacecraft when being positioned at a measurement and control boundary
In the station coordinate system, spacecraft position vector r t Can be expressed as:
the track plane normal vector h can be expressed as:
note that |h|=rcosα, normalized by h yields a unit vector:
(3) solving for the variable θ using equality constraints
In the coordinate system of the measuring station, the unit vector z corresponding to the z axis of the fixed coordinate system can be expressed as:
the included angle between the normal unit vector h of the track surface and the unit vector z is the track inclination angle i, and can be determined by the following formula:
θ can be solved according to the above:
wherein the value range of the inverse cosine function is [0, pi ]]Two solutions of θ obtained in the formula 1 、θ 3 Corresponding to the spacecraft circle satellite point tracks L which just pass through the measurement and control boundary respectively 1 And L 3 The method comprises the steps of carrying out a first treatment on the surface of the L can be obtained by a similar method 2 And L 4 Corresponding theta 2 、θ 4 。
(4) Calculating track lifting intersection longitude
The coordinate system descending intersection vector N can be obtained by the following formula:
the track lifting intersection longitude Ω' is obtained from the following two:
by solving for θ by two solutions of θ 1 、θ 3 Substituting formula I and finding omega 'from formula II' 1 、Ω′ 3 ；
(5) Calculating latitude amplitude angle of spacecraft when being positioned at measurement and control boundary
The latitude amplitude angle phi is an ascending intersection line vector N and a spacecraft position vector r t The included angle between the two parts is that,
and (5) obtaining the inverse cosine:
when the measuring station is positioned in the northern hemisphere, the value range of the inverse cosine function is [0, pi ]]Through two solutions of θ 1 、θ 3 Substitution to obtain two solutions of phi 1 、Φ 3 ；
(6) Calculating the longitude of the ascending intersection point of the track of the point under the satellite
Considering the rotation of the earth and the right ascent and descent of the orbit intersection point of the spacecraft, the longitude of the orbit intersection point of the satellite point of the spacecraft is not equal to the longitude of the orbit intersection point, the latitude amplitude angle when the spacecraft passes the boundary of the measuring station is phi, and the orbit period is T, the time difference deltat between the moment of the orbit intersection point of the spacecraft passing the circle and the current moment is known as:
when the spacecraft passes the station boundary, the longitude of the orbit intersection point is omega', and when the longitude of the orbit intersection point of the ring star lower point is omega:
wherein omega e Is the rotation angular rate of the earth;
for increasing the intersection right-hand drift rate, it is determined by the following formula:
wherein a is e The radius of the equator of the earth, a is the semilong axis of the orbit, e is the eccentricity of the orbit, and the unit of the above formula is (°)/d;
by the steps (1) to (6), the boundary rise intersection point longitude Ω of the spacecraft t that can be observed by the station S is obtained 1 And omega 3 。
The following is the loop solving process of the spacecraft station.
T is known to be 0 The longitude of the orbit ascending intersection point of the time spacecraft is omega' 0 The track circle number is N 0 If the test station passes through n more turns, the future turn number of the test station can be obtained by the following formula:
after N is solved by the method, the number of times of the station can be measured to be N 0 +n。
The following is a spacecraft earth center distance solving process.
In this step, it is assumed that the ground center distance when the observed spacecraft t passes the station is r (for a near circular orbit, the semi-major axis a may be used instead). For circular tracks, the geocentric distance is equivalent to the semi-long axis; there is a slight difference between the elliptical orbits of the near circles. If the true ground center distance is used in the solving process instead of directly replacing the true ground center distance with the semi-long axis a, the solving result is more accurate. The determination of the geodesic distance r when the spacecraft passes the station is given here.
In a strict sense, when the spacecraft is at different positions of the measurement and control area, the corresponding geocentric distances are different. However, the method uses the geodesic distance at the top of the station to represent the geodesic distance of all the stations. The method comprises the following steps: the semi-long axis of the observed spacecraft t is known as a, the orbit inclination is i, the eccentricity is e, and the perigee amplitude is ω. And solving the geodesic distance r when the spacecraft passes through the station.
When the spacecraft passes through the station roof, the vector pointing to the spacecraft from the station is r s . At this time, r s Is located in the plane of the spacecraft orbit. In the station coordinate system, the normal unit vector of the spacecraft orbit can be expressed as
Wherein θ is r xy And y is s The included angle of the axes is a free variable,
the track tilt i versus h, z can be expressed as:
from the above, θ can be found as:
the ascending intersection line N of the spacecraft orbit is as follows:
when the measuring station is positioned in the northern hemisphere, the latitude amplitude angle phi when the spacecraft passes the measuring station top is as follows:
the ground center distance when the spacecraft passes the station is as follows:
c. and c, performing measurement and control coverage calculation according to the measurement and control coverage boundary conditions in the step b, wherein the calculation comprises the following steps: according to the circle number, the latitude amplitude angle and the geocentric distance obtained in the step b when the station is overstepped, the orbit of the spacecraft is directly extrapolated to the rough moment of the station by utilizing an autonomous orbit forecasting algorithm; and on the basis of the rough moment of the station passing by, the moment of entering and exiting the station and the station passing time are accurately calculated.
After the spacecraft orbit is fixed at any moment, the orbit number passing through a specific measuring station in the future can be rapidly obtained. To further get the specific time to get in and out the station, this step solves 2 problems: firstly, how to rapidly extrapolate the track to the moment before the circle of the overstepping station approaches the overstepping station, which involves the problem of track forecasting; and secondly, accurately calculating the time for entering and exiting the measuring station, namely measuring and controlling the coverage solving problem.
The following is a further explanation regarding autonomous orbit forecasting.
Due to the on-orbit computational power limitations, the method of numerical integration orbit perturbation equations in the usual case cannot be used for orbit extrapolation. Here, the trajectory is extrapolated using an analytical method.
Because the manned spacecraft flies in the near-ground orbit, the eccentricity is smaller, singular points can appear when the orbit extrapolation is performed by using an analytic method, and the orbit extrapolation is suitable for using a pseudo-average root number method to avoid the phenomenon. And constructing a first kind of non-singular variables according to the number of the kepler orbits.
For global aspheric gravitational perturbation, the non-singular perturbation solution is expressed as formula three:
in the first order sense, the form is of formula four:
wherein sigma (t) is the instantaneous orbit number,
for the average number of tracks, < > is->
Is a first order short period term,/->
Is a second-order short period term, sigma 1 As a first-order long term, sigma 2 For long term of second order>
Is a first-order long period term, t 0 Indicating the initial time.
The low-orbit manned spacecraft needs to consider the atmospheric resistance, and an average density model can be adopted to construct an atmospheric resistance perturbation solution; and substituting the atmospheric resistance perturbation as a second-order long-term into the formula 1 in the fourth, and obtaining an orbit extrapolation analytical expression considering the global aspheric gravitation and the atmospheric resistance.
The autonomous orbit prediction procedure is thus available as follows: when the spacecraft obtains t through autonomous orbit determination 0 Instantaneous orbit root sigma of moment 0 Then, the average track number corresponding to the moment is obtained by the 3 rd expression in the fourth expression
Obtaining the average track number of any time t according to the 1 st expression and each order perturbation expression in the fourth expression>
Finally, the instantaneous orbit root sigma (t) at the moment t is obtained according to the formula III.
The following is the measurement and control coverage solution process.
Calculating the time for entering and exiting the measuring station, namely solving the time period that the elevation angle of the spacecraft relative to the measuring station is larger than the lowest elevation angle alpha of the measuring station,
from the geometrical relationship in fig. 2, the elevation angle of the spacecraft with respect to the station at any time is:
the whole process of spacecraft orbit propulsion is discretized into m equal parts, namely m+1 discrete points, and the corresponding time sequence is recorded as t i I=1, 2, …, m+1; obtaining the difference delta between the elevation angle of the spacecraft relative to the measuring station at m+1 points and the minimum observation elevation angle; when delta i Not less than 0 and delta i-1 <At 0, t i The time for starting measurement and control; when delta i <0 and delta i-1 When not less than 0, t i The time of the end of measurement and control; because of the discrete processing, only a conservative estimation of the actual measurement and control start or end time is performed, and for better approximation, linear interpolation can be performed, wherein the actual measurement and control start or end time is t' i This time must be in interval t i-1 ，t i ]In, the corresponding elevation angle difference is 0, and the following conditions are satisfied on the premise that the elevation angle linearly changes along with time:
thereby obtaining the following steps:
according to the spacecraft autonomous measurement and control coverage analysis method, the orbit circle number and latitude amplitude range of a future over-measurement station of the spacecraft are determined by solving the measurement and control boundary conditions of the over-measurement station; the orbit of the spacecraft is directly extrapolated to the station-passing moment from the current moment by using the extrapolation of the orbit of the analytic method, and the time for entering and exiting the station is accurately calculated on the basis. The algorithm only involves simple matrix operation and trigonometric function operation, avoids numerical integration and point-by-point measurement and control coverage analysis, greatly reduces the calculated amount and improves the reliability. The method is suitable for on-orbit autonomous measurement and control coverage analysis of the spacecraft.
The above description is only one embodiment of the present invention and is not intended to limit the present invention, and various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A spacecraft autonomous measurement and control coverage analysis method comprises the following steps:
a. establishing a ground station coordinate system for describing relative station movement of a spacecraft to a ground designated point, establishing a geocentric equatorial fixed coordinate system, and establishing an orthogonal transformation matrix from the station coordinate system to the fixed coordinate system;
b. calculating boundary conditions of the spacecraft which can be covered by the measuring station;
c. performing measurement and control coverage calculation according to the measurement and control coverage boundary conditions in the step b;
in the step b, according to the parameters of the station under the fixed connection coordinate system and the orbit parameters of the observed spacecraft, solving the longitude and latitude amplitude angles of the boundary lifting intersection point which can be observed by the station of the spacecraft, and obtaining the future circle number of the station of the spacecraft;
according to the orbit parameters of the observed spacecraft, solving the earth center distance when the spacecraft passes through the station;
in the step b, solving the measurement and control coverage boundary condition of a single measuring station on the spacecraft, and solving the longitude omega of the intersection point of the trajectory rise of the point under the boundary satellite, which can be observed by the measuring station S, and the corresponding latitude amplitude phi according to the position of the measuring station S, the lowest measurement and control elevation angle alpha and the orbit number of the observed spacecraft t;
in the step c, according to the circle number, the latitude amplitude angle and the geodesic distance obtained in the step b when the station is overstepped, the orbit of the spacecraft is directly extrapolated to the rough moment of the station by using an autonomous orbit forecasting algorithm; on the basis of the rough moment of the station passing through, the moment of entering and exiting the station and the station passing time are accurately calculated;
in the step c, autonomous orbit prediction is included, and orbit extrapolation is carried out by adopting a pseudo-average root number method;
for global aspheric gravitational perturbation, the non-singular perturbation solution is expressed as formula three:
in the first order sense, the form is of formula four:
wherein sigma (t) is the instantaneous orbit number,
for the average number of tracks, < > is->
Is a first order short period term,/->
Is a second-order short period term, sigma 1 As a first-order long term, sigma 2 For long term of second order>
Is a first-order long period term, t 0 Representing an initial time;
the low-orbit manned spacecraft needs to consider the atmospheric resistance, and an average density model can be adopted to construct an atmospheric resistance perturbation solution; substituting the atmospheric resistance perturbation as a second-order long term into the formula 1 in the fourth, so as to obtain an orbit extrapolation analytical expression considering the global aspheric gravitation and the atmospheric resistance;
the autonomous orbit prediction procedure is thus available as follows: when the spacecraft obtains t through autonomous orbit determination 0 Instantaneous orbit root sigma of moment 0 Then, the average track number corresponding to the moment is obtained through the 3 rd formula in the fourth formula
Obtaining the average track number of any time t according to the 1 st expression and each order perturbation expression in the fourth expression>
Finally, obtaining an instantaneous orbit root sigma (t) at a moment t according to the third step;
in the step c, calculating the time for entering and exiting the station, namely solving the time period that the elevation angle of the spacecraft relative to the station is larger than the lowest elevation angle alpha of the station;
the elevation angle of the spacecraft at any moment relative to the measuring station is as follows:
the whole process of spacecraft orbit propulsion is discretized into m equal parts, namely m+1 discrete points, and the corresponding time sequence is recorded as t i I=1, 2, …, m+1; obtaining elevation angles and the most elevation angles of the spacecraft relative to the measuring station at m+1 pointsSmall difference in elevation delta; when delta i Not less than 0 and delta i-1 <At 0, t i The time for starting measurement and control; when delta i <0 and delta i-1 When not less than 0, t i The time of the end of measurement and control; because of the discrete processing, only a conservative estimation of the actual measurement and control start or end time is performed, and for better approximation, linear interpolation can be performed, wherein the actual measurement and control start or end time is t' i This time must be in interval t i-1 ，t i ]In, the corresponding elevation angle difference is 0, and the following conditions are satisfied on the premise that the elevation angle linearly changes along with time:
thereby obtaining the following steps:
2. the spacecraft autonomous measurement coverage analysis method according to claim 1, wherein in the step a, the station coordinate system is used for describing the movement of the spacecraft relative to a station for a ground designated point; origin o of coordinate system of measuring station s Taking the center of the measuring station and z when the earth is spherical s The axis points from the earth center to the zenith, x s Axis, y s The axis is positioned in the local horizontal plane, is parallel to the meridian line and the weft line of the passing station respectively, and points to the eastern and the north respectively;
the reference plane of the fixedly connected coordinate system is a protocol equatorial plane, the x-axis points to the Greennel meridian, the z-axis points to the international protocol origin CIO, and the x-axis, the y-axis and the z-axis form a right-hand system;
the longitude of the measuring station under the fixed coordinate system is lambda, and the latitude is
And when the average radius of the earth is R, the orthogonal transformation matrix E from the station coordinate system to the fixed coordinate system is as follows:
vector r of geodetic centre pointing to measuring station s The attached coordinate system can be expressed as:
3. the spacecraft autonomous measurement coverage analysis method of claim 1, wherein boundary orbit parameters are solved: longitude lambda and latitude of measuring station S under fixed coordinate system
The lowest elevation angle of the station is alpha; the ground center distance of the observed spacecraft t is r, the orbit inclination angle is i, and the longitude omega of the boundary lifting intersection point observed by the observed station S of the spacecraft t is solved 1 And omega 3 The method is characterized by comprising the following steps:
(1) solving unit speed vector v of spacecraft when being positioned at measurement and control boundary
In the coordinate system of the measuring station, the vector r of the measuring station pointing to the spacecraft st Can be expressed as:
wherein the variable θ is introduced, defined as r xy And y is s An included angle of the shaft;
in the coordinate system of the measuring station, the measuring station position vector r s Can be expressed as:
wherein R is the average radius of the earth;
in the station coordinate system, the unit velocity vector v can be expressed as:
(2) solving a normal vector h of a track surface of the spacecraft when being positioned at a measurement and control boundary
In the station coordinate system, spacecraft position vector r t Can be expressed as:
the track plane normal vector h can be expressed as:
note that |h|=rcosα, normalized by h yields a unit vector:
(3) solving for the variable θ using equality constraints
In the coordinate system of the measuring station, the unit vector z corresponding to the z axis of the fixed coordinate system can be expressed as:
the included angle between the normal unit vector h of the track surface and the unit vector z is the track inclination angle i, and can be determined by the following formula:
θ can be solved according to the above:
wherein the value range of the inverse cosine function is [0, pi ]]Two solutions of θ obtained in the formula 1 、θ 3 Corresponding to the spacecraft circle satellite point tracks L which just pass through the measurement and control boundary respectively 1 And L 3 ；
(4) Calculating track lifting intersection longitude
The coordinate system descending intersection vector N can be obtained by the following formula:
the track lifting intersection longitude Ω' is obtained from the following two:
by solving for θ by two solutions of θ 1 、θ 3 Substituting formula I and finding omega 'from formula II' 1 、Ω′ 3 ；
(5) Calculating latitude amplitude angle of spacecraft when being positioned at measurement and control boundary
The latitude amplitude angle phi is an ascending intersection line vector N and a spacecraft position vector r t The included angle between the two parts is that,
and (5) obtaining the inverse cosine:
when the measuring station is positioned in the northern hemisphere, the value range of the inverse cosine function is [0, pi ]]Through two solutions of θ 1 、θ 3 Substitution to obtain two solutions of phi 1 、Φ 3 ；
(6) Calculating the longitude of the ascending intersection point of the track of the point under the satellite
Considering the rotation of the earth and the right ascent and descent of the orbit intersection point of the spacecraft, the longitude of the orbit intersection point of the satellite point of the spacecraft is not equal to the longitude of the orbit intersection point, the latitude amplitude angle when the spacecraft passes the boundary of the measuring station is phi, and the orbit period is T, the time difference deltat between the moment of the orbit intersection point of the spacecraft passing the circle and the current moment is known as:
when the spacecraft passes the station boundary, the longitude of the orbit intersection point is omega', and when the longitude of the orbit intersection point of the ring star lower point is omega:
wherein omega e Is the rotation angular rate of the earth;
for increasing the intersection right-hand drift rate, it is determined by the following formula:
wherein a is e The radius of the equator of the earth, a is the semilong axis of the orbit, e is the eccentricity of the orbit, and the unit of the above formula is (°)/d;
by the steps (1) to (6), the boundary rise intersection point longitude Ω of the spacecraft t that can be observed by the station S is obtained 1 And omega 3 。
4. The spacecraft autonomous measurement coverage analysis method of claim 3, wherein the number of turns of a spacecraft transit station is solved: t is t 0 The longitude of the orbit ascending intersection point of the time spacecraft is omega' 0 The track circle number is N 0 After n more turns, the future turn number of the passing measuring station can be obtained by the following formula:
after N is solved by the method, the number of times of the station can be measured to be N 0 +n。
5. The spacecraft autonomous measurement coverage analysis method of claim 4, wherein the spacecraft ground center distance is solved: when the spacecraft passes through the station roof, the vector pointing to the spacecraft from the station is r s At this time, r s In the plane of the spacecraft orbit, in the station coordinate system, the normal unit vector of the spacecraft orbit can be expressed as:
wherein θ is a free variable;
the relationship between the track inclination angles i and h and the unit vector z corresponding to the z axis of the fixed coordinate system can be expressed as follows:
θ can be obtained from the above:
the ascending intersection line N of the spacecraft orbit is as follows:
when the measuring station is positioned in the northern hemisphere, the latitude amplitude angle phi when the spacecraft passes the measuring station top is as follows:
the ground center distance when the spacecraft passes the station is as follows:
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